Vibrational modes of Skyrmions

Abstract

We study the vibrational modes of Skyrmions with baryon numbers one through eight in the standard Skyrme model. The vibrational modes are found in the harmonic approximation around the classical soliton solution and the real parts of the frequencies of the modes are extracted. We further classify the vibrational modes into representations of the symmetries possessed by the Skyrmion solutions. We find that there are approximately 7B low-lying modes for a Skyrmion with baryon number B, in addition to an infinite continuum of scattering modes. This result suggests that the instanton moduli space, which is 8B-dimensional, does not accurately describe the deformation space of Skyrmions as previously conjectured.

arXiv comment10+10 pages, 3 figures, animations of the modes available at http://www1.maths.leeds.ac.uk/pure/geometry/SkyrmionVibrations/

References in corpus (25)

• Quasi-Normal Modes of Stars and Black Holes
• Rational Maps, Monopoles and Skyrmions
• A Skyrme-type proposal for baryonic matter
• Skyrmions with low binding energies
• Light Nuclei as Quantized Skyrmions
• Resonant kink-antikink scattering through quasinormal modes
• A dynamical $\alpha$-cluster model of ${}^{16}$O
• Attractive Channel Skyrmions and the Deuteron
• Vibrational quantisation of the B=7 Skyrmion
• Monopole Scattering with a Twist
• Loosening up the Skyrme model
• Generalized Skyrme model with the loosely bound potential
• Normal Mode Spectrum of the Deuteron in the Skyrme Model
• Symmetric Instantons and Skyrme Fields
• Normal Modes of the B=4 Skyrme Soliton
• Skyrmions in models with pions and rho mesons
• Modifying the pion mass in the loosely bound Skyrme model
• An Alpha Particle Model for Carbon-12
• Exploring the generalized loosely bound Skyrme model
• A higher-order Skyrme model
• Instanton vibrations of the 3-Skyrmion
• Skyrmion Vibration Modes within the Rational Map Ansatz
• Radial vibrations of BPS skyrmions
• Roper resonances and quasi-normal modes of Skyrmions
• Stability of the B=2 hedgehog in the Skyrme model

Cited by in corpus (22)

• Topological spin Hall effects and tunable skyrmion Hall effects in uniaxial antiferromagnetic insulators
• Spectral walls in multifield kink dynamics
• Kink-antikink collisions in a weakly interacting ${\varphi }^4$ model
• A new consistent Neutron Star Equation of State from a Generalized Skyrme model
• Realistic classical binding energies in the $\omega$-Skyrme model
• Spectral Walls at One Loop
• A Smörgåsbord of Skyrmions
• Coriolis terms in Skyrmion Quantization
• Quasi-universal relations for generalized Skyrme stars
• Quantum binding energies in the Skyrme model
• ADHM skyrmions
• Neutron stars within the Skyrme model
• Dielectric Skyrmions
• A consistent two-skyrmion configuration space from instantons
• The Inevitability of Sphalerons in Field Theory
• Quantum soliton scattering manifolds
• Near-BPS Skyrmions
• Nonlinear rigid-body quantization of Skyrmions
• Adding crust to BPS Skyrme neutron stars
• Compressibility of dense nuclear matter in the $\rho$-meson variant of the Skyrme model
• Quantization of skyrmions using instantons
• Modes of the Sakai-Sugimoto soliton